On the geometry of quantum states

Journal Article · Wed Jan 31 23:00:00 EST 1996 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.49720· OSTI ID:401051

Aguilar, M A ^[1]; Socolovsky, M ^[2]

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1. Instituto de Matematicas (Mexico)
2. Instituto de Ciencias Nucleares, UNAM, Cd. Universitaria, 04510 (Mexico), D.F.

Using category theory we show that basic elements of quantum theory, like complexifications, Clifford algebras and projective spaces, appear naturally as universal objects of functors. We give the homotopy equivalence between the {ital U}(1)-classifying bundle in topology and the projective bundle associated with a separable Hilbert space. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 401051
• Report Number(s): CONF-9511225--
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 359; ISSN 0094-243X; ISSN APCPCS
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLIFFORD ALGEBRA
ENERGY LEVELS
GEOMETRY
HILBERT SPACE
INVARIANCE PRINCIPLES
QUANTUM MECHANICS
U-1 GROUPS